The $r$ -Restricted Connectivity of Hyper Petersen Graphs

The connectivity of a multiprocessor system or an interconnection network plays an important role in measuring the fault tolerance of the network. As a famous topology structure of interconnection networks, the hyper petersen graph HPn has many good properties. In this paper, we show that the r-restricted connectivity of HP
_n
is -1/2r
²
+ (n - 3/2)r + n and HP
_n
is two super r-restricted connected for n ≥ 4 and 0 ≤ r ≤ n - 3.